Honors Geometry Syllabus CHS Mathematics Department

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1 1 Honors Geometry Syllabus CHS Mathematics Department Contact Information: Parents may contact me by phone, or visiting the school. Teacher: Mr. Seth Moore Address: Phone Number: (740) ext Online: CHS Vision Statement: Our vision is to be a caring learning center respected for its comprehensive excellence. CHS Mission Statement: Our mission is to prepare our students to serve their communities and to commit to life-long learning Course Description and Prerequisite(s) from Course Handbook: Honors Geometry -272 State Course # Prerequisite: Students must have attained a B+ or better in Algebra I and teacher approval Required Option Grade: 9-10 Weighted Grade Credit: 1 This course is design for the advanced math student. It will cover the same topics as Geometry, with an accelerated pace and expectations of deeper understanding. In-depth study of two and three-dimensional geometry including representing problem situations using geometric models, deductive reasoning, and geometry from an algebraic perspective. The fundamental purpose of the course in Geometry is to formalize and extend students geometric experiences from the middle grades. Students explore more complex geometric situations and deepen their explanations of geometric relationships, moving towards formal mathematical arguments. Important differences exist between this Geometry course and the historical approach taken in Geometry classes. For example, transformations are emphasized dearly in this course. Close attention should be paid to the introductory content for the Geometry conceptual category found in the high school CCSS. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

2 2 Big Ideas/Purpose per Unit and Essential Questions/Concepts per Unit: Defined below for clarity are the Big Ideas/Purpose of every unit taught during this course and the essential questions/concepts to be learned to better understand the Big Ideas/Purpose. A student s ability to grasp, answer, and apply the essential questions/concepts will define whether or not he or she adequately learns the Big Ideas/Purpose and scores well on assessments given for this course. The Common Core Standards can be found at 1 st or 3 rd 9 Weeks: o Unit I: Proof and Parallel and Perpendicular Lines Big Idea #1: Prove theorems about lines and angles. Essential Question #1: Why is it important to be able to prove theorems about lines and angles? Essential Question #2: How are vertical angles proven congruent? Essential Question #3: What effect does a perpendicular bisector have on a line segment? Essential Question #4: How is a point on a directed line segment between two given points that partition the segment in a given ration found? Big Idea #2: Prove parallel and perpendicular lines Essential Question #1: What can be proven congruent when parallel lines are cut by a transversal? Essential Question #2: How can the slope criteria for parallel and perpendicular lines be used to prove lines are parallel or perpendicular? Essential Question #3: How can the equation of a line parallel or perpendicular to a given line that passes through a given point be determined? Essential Question #4: How are lines proven to be parallel? o Unit II: Triangles Big Idea #1: Prove theorems about triangles and congruency in triangles Essential Question #1: How are the interior angles of a triangle proven to measure 180? Essential Question #2: How are two triangles proven congruent to one another? Essential Question #3: How are the base angles of an isosceles triangle proven to be congruent? Essential Question #4: How can the definition of congruence in terms of rigid motion be used to show that two triangles are congruent if and only if

3 3 corresponding pairs of sides and corresponding pairs of angles are congruent? Big Idea #2: Understand and prove relationships in triangles Essential Question #1: What are the similarities and differences of a circumcenter, incenter, orthocenter, and centroid? Essential Question #2:How is it proven that the perpendicular bisectors, angle bisectors, medians, or altitudes of a triangle all meet at a common point? Essential Question #3: How is it proven that the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length? Essential Question #4: How are inequalities used in triangles and why are they important? o Unit III: Quadrilaterals Big Idea #1: Classify and prove theorems about quadrilaterals Essential Question #1: How are quadrilaterals classified and what are the properties of each? Essential Question #2: How are opposite sides of a parallelogram proven congruent? Essential Question #3: How are opposite angles of a parallelogram proven congruent? Essential Question #4: How is it proven that the diagonals of a parallelogram bisect each other? Essential Question #5: How can properties, theorems, corollaries, and definitions be used to prove definitions of quadrilaterals? Essential Question #6: How can coordinate geometry be used to prove general relationships about quadrilaterals? 2 nd or 4 th 9 Weeks: o Unit IV: Similarity and Transformations Big Idea #1: Prove theorems involving similarity Essential Question #1: Given two figures, how can the definition of similarity in terms of similarity transformations decide if geometric figures are similar? Essential Question #2: How can proportions, angle measures, and properties be used to prove triangles similar?

4 4 Essential Question #3: How can congruence and similarity criteria for triangles be used to solve problems? Essential Question #4: How can the theorem a line parallel to one side of a triangle divides the other two proportionally be proven? Big Idea #2: Understand and apply transformations Essential Question #1: What is the effect of a translation, reflection, or rotation on a geometric figure? Essential Question #2: How can a composition of transformations create a congruent figure? Essential Question #3: Given two figures, how can the definition of congruence in terms of rigid motion be used to decide if they are congruent? Essential Question #4: How does a dilation affect a figure? Essential Question #5: Given the center and scale factor, how can a dilation s properties be verified experimentally? Big Idea #3: Understand similarity in terms of similarity transformations Essential Question #1: In a dilation, why does a line not passing through the center of the dilation to a parallel line leave a line passing through the center unchanged? Essential Question #2: In a dilation, why is a line segment longer or shorter in the ratio given by the scale factor? Essential Question #3: Given two figures, how is the definition of similarity in terms of similarity transformations used to decide if they are similar? Essential Question #4: How is are the properties of similarity transformations used to establish the AA criterion for two triangles to be similar? o Unit V: Trigonometry and Circles Big Idea #1: Use the Pythagorean Theorem to solve right triangles in applied problems Essential Question #1: How is the Pythagorean Theorem and its converse derived and applied? Essential Question #2: How does the Pythagorean Theorem apply to and triangles? Essential Question #3: How can the Pythagorean Theorem be used to solve real world problems

5 5 Big Idea #2: Understand and apply trigonometric ratios Essential Question #1: How is similarity used to find the definitions of trigonometric ratios for acute angles? Essential Question #2: How can the relationship between the sine and cosine of complementary angles be explained and used? Essential Question #3: How can the trigonometric ratios be used to solve real world problems? Essential Question #4: How can trigonometric ratios be applied to angles of elevation and angles of depression? Big Idea #3: Understand and apply theorems about circles Essential Question #1: How can all circles be proven similar? Essential Question #2: What are the relationships among inscribed angles, radii, and chords? Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. Essential Question #3: How are the inscribed and circumscribed circles of a triangle constructed? Essential Question #4: How are the properties of angles for a quadrilateral inscribed in a circle proven? Essential Question #5: How can the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality both be derived using similarity? Big Idea #4: Translate between the geometric description and the equation of a circle. Essential Question #1: Given the center of a circle and its radius, how can the equation of the circle be derived? Essential Question #2: Given a circle in the coordinate plane, how is its equation derived? Essential Question #3: How can completing the square be used to find the center and radius of a circle given by an equation? o Unit VI: Area and Extending to Three Dimensions

6 6 Big Idea #1: Visualize relationships between twodimensional and three-dimensional objects Essential Question #1: How are the shapes of twodimensional cross-sections of three-dimensional objects identified? Essential Question #2: How are three-dimensional objects generated by rotations of two-dimensional objects identified? Big Idea #2: Understanding and deriving area formulas Essential Question #1: How is an informal argument for the formulas for the circumference of a circle, area of a circle found? Essential Question #2: How is the formula for the area of a sector derived? Essential Question #3: How can coordinates be used to compute perimeters and areas of polygons? Essential Question #4: How are concepts of density based on area and volume in modeling situations applied to real world situations? Essential Question #5: How are geometric methods applied to solve real world area design problems? Big Idea #3: Explain volume formulas and use them to solve problems Essential Question #1: How is an informal argument for the formulas for the volume of a cylinder, pyramid, and cone found? Essential Question #3: How are volume formulas for cylinders, pyramids, cones, and spheres used to solve problems? Essential Question #3: How are geometric shapes, their measures, and their properties used to describe three-dimensional objects? Essential Question #3: How are geometric methods applied to solve real world volume design problems? End of Course Exam Textbook: Carter, J. A., & Cuevas, G. J. (2014). Glencoe Geometry (Common Core Ed.). Columbus, OH: McGraw-Hill Companies. Supplemental Textbook(s): Supplemental materials will be used throughout the school year. However, no additional textbooks will be distributed to students.

7 7 Course Expectations Class Rules 1.) Be punctual 2.) Be prepared for class 3.) Be respectful towards teachers/staff, class members, school property, etc. 4.) Be honest 5.) Be observant of all class, school, and district rules and policies 6.) Be positive Procedures 1.) Students will write and perform Bellringer, write the essential question(s), and get materials ready the first 3 minutes of class 2.) Students will request permission from the teacher, get their agenda signed, and sign out on the back of the door to leave the classroom for any reason 3.) Students will turn in work at the appropriate time and place 4.) Students will clean up after themselves as well as their group members 5.) Students will remain seated in their assigned seat unless otherwise given permission 6.) Students are responsible for getting their make-up work after an absence 7.) Students are responsible for scheduling make-up tests and quizzes with the teacher Course Material 3-ring Binder with Dividers Loose Leaf College Ruled Paper Pencils Colored Pencils Graph Paper Scientific or Graphing Calculator (TI-84+is recommended) Compass Protractor Ruler Grading: Explaining the process of Mathematics is essential for success in this class and standardized tests. Therefore, all work must be shown algebraically to receive full credit. Summative Unit Assessments 50%

8 8 Assessments 30% Classwork 10% Homework 10% Grading Scale The grading scale for Chillicothe High School can be found in the student handbook. Late Work: Late work will be subject to the board adopted policy on assignments that are turned in late (to be reviewed in class). CHS TENTATIVE Course Schedule This is an overview of what will be covered in this course at CHS for this school year. Although, I would like to follow this plan verbatim this years tentative schedule is subject to change (at the teachers discretion). 1 st or 3 rd 9 Weeks: Week 1: Beginning of the Year Pre-Assessment Exam Weeks 1-3: Unit 1 Proof and Parallel and Perpendicular Lines 2.5 Postulates and Paragraph Proofs 2.6 Algebraic Proof 2.7 Proving Segment Relationships 2.8 Proving Angle Relationships 3.1 Parallel Lines and Transversals Explore: Angles and Parallel Lines 3.2 Angles and Parallel Lines 3.3 Slopes of Lines 3.4 Equations of Lines Extend: Equations of Perpendicular Bisectors 3.5 Proving Lines Parallel 3.6 Perpendiculars and Distance Weeks 4-7: Unit 2 Triangles 4.1 Classifying Triangles 4.2. Angles in Triangles 4.3 Congruent Triangles 4.4 Proving Triangles Congruent SSS,SAS Extend: Proving Constructions 4.5 Proving Triangles Congruent ASA, AAS Extend: Congruence in Right Triangles 4.6 Isosceles and Equilateral Triangles Explore: Congruence Transformations 4.7 Congruence Transformations 4.8 Triangles and coordinate Proof Chapter 5 Explore: Construction Bisectors

9 9 5.1 Bisectors of Triangles Explore: Constructing Medians and Altitudes 5.2 Medians and Altitudes of Triangles 5.3 Inequalities in One Triangle 5.4 Indirect Proof Explore: The Triangle Inequality 5.5 The Triangle Inequality 5.6 Inequalities in Two Triangles Weeks 8-9: Unit 3 Quadrilaterals 6.1 Angles of Polygons Extend: Angles of Polygons 6.2 Parallelograms Explore: Parallelograms 6.3 Tests for Parallelograms 6.4 Rectangles 6.5 Rhombi and Squares 6.6 Trapezoids and Kites 2 nd or 4 th 9 Weeks: Week 1-3: Unit 4 Similarity and Transformations 7.1 Ratios and Proportions 7.2 Similar Polygons 7.3 Similar Triangles Extend: Proofs of Perpendicular and Parallel Lines 7.4 Parallel Lines and Proportional Parts 7.5 Parts of Similar Triangles 7.6 Similarity Transformations 7.7 Scale Drawings and Models 9.1 Reflections 9.2 Translations Explore: Rotations 9.3 Rotations Extend: Solids of revolution Explore: Compositions of Transformations 9.4 Compositions of Transformations 9.5 Symmetry Extend: Constructions with a Reflective Device Explore: Dilations 9.6 Dilations Extend: Establishing Triangle Congruence and Similarity Week 4-6: Unit 5 Trigonometry and Circles 8.2 The Pythagorean Theorem and Its Converse 8.3 Special Right Triangles Explore: Trigonometry

10 Trigonometry 8.5 Angles of Elevation and Depression 10.1 Circles and Circumference 10.2 Measuring Angles and Arcs 10.3 Arcs and Chords 10.4 Inscribed Angles 10.5 Tangents Extend: Inscribed and Circumscribed Circles 10.6 Secants, Tangents, and Angle Measures 10.7 Special Segments in a Circle 10.8 Equations of Circles Week 7-9: Unit 6 Area and Extending to Three Dimensions 11.1 Areas of Parallelograms and Triangles Explore: Areas of Trapezoids, Rhombi, and Kites 11.2 Areas of Trapezoids, Rhombi, and Kites Extend: Population Density 11.3 Areas of Circles and Sectors Explore: Investigating Areas of Regular Polygons 11.4 Areas of Regular Polygons and Composite Figures Extend: Regular Polygons on the Coordinate Plane 11.5 Areas of Similar Figures 12.1 Representations of Three-Dimensional Figures Extend: Topographic Maps 12.2 Surface Areas of Prisms and Cylinders 12.3 Surface Areas of Pyramids and Cones 12.4 Volumes of Prisms and Cylinders Extend: Changing Dimensions 12.5 Volumes of Pyramids and Cones 12.6 Surface Area and Volumes of Spheres 12.7 Spherical Geometry Extend: Navigational Coordinates 12.8 Congruent and Similar Solids End of Course Exam Performance Based Section: Writing Assignments/Exams/Presentations/Technology One or more of the End of Unit Exams may be Performance Based. According to the Ohio Department of Education, Performance Based Assessments (PBA) provides authentic ways for students to demonstrate and apply their understanding of the content and skills within the standards. The performance based assessments will provide formative and summative information to inform instructional decision-making and help students move forward on their trajectory of learning. Some examples of Performance

11 11 Based Assessments include but are not limited to portfolios, experiments, group projects, demonstrations, essays, and presentations. CHS Honors Geometry Course Syllabus After you have reviewed the preceding packet of information with your parent(s) or guardian(s), please sign this sheet and return it to me so that I can verify you understand what I expect out of each and every one of my students. Student Name (please print): Student Signature: Parent/Guardian Name (please print): Parent/Guardian Signature: Date: